Dipartimenti di Matematica, Aula Seminari.<\/p>\n
Our main result provides a condition under which the partition regularity (PR) of systems of functional equations over a given infinite set can be completely characterised by the existence of constant solutions. From this result, we characterise the PR of several families of non-linear equations over infinite subsets of $\\mathbb C$, such as $\\mathbb N$, $\\mathbb Z$ or finitely generated multiplicative subgroups of $\\mathbb C^\\times$. Examples of applications of our main theorem includes:<\/p>\n
1. A complete characterisation of the PR system polynomial equations in two variables over $\\mathbb N$;
2. a complete characterisation of the PR of polyexponential equations over $\\mathbb Z$;
3. a complete characterization of the PR of Thue-Mahler equations over $\\mathbb Z$; and
4. the failure of Rado’s Theorem for linear equations over finitely generated subgroups of $\\mathbb C^\\times$.
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Joint work with Lorenzo Luperi Baglini.<\/p>\n
Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" Our main result provides a condition under which the partition regularity (PR) of systems of functional equations over a given infinite set can be completely characterised by the existence of constant solutions. From this result, we characterise the…<\/p>\n